Sources told ESPN.com that discussions are underway between the two parties, but Tennessee still has an opportunity to keep Martin.
Marquette is pursuing a replacement for Buzz Williams, who left after six seasons to take over as coach at Virginia Tech.
Martin's buyout with the Vols goes down from $2.6 million to $1.3 million on April 1, according to a source.
Martin led Tennessee to a 24-13 record this season, 11-7 in the SEC. The Vols lost to Michigan in the Sweet 16 on Friday in Indianapolis after beating Iowa in the First Four in Dayton then UMass and Mercer in the rounds of 64 and 32, respectively, in Raleigh last week.
Martin, who took the Vols to the NIT in his first two seasons in Knoxville after replacing Bruce Pearl, played at Purdue and was a head coach at Missouri State before landing at Tennessee. Martin's Midwestern roots make him a solid fit for the Milwaukee-based school.
Marquette interim athletic director Bill Cords is conducting the search for the Golden Eagles.
Former UCLA coach Ben Howland and current Duke assistant Steve Wojciechowski have also been considered for the job, sources have told ESPN.com.
ESPN.com's Jeff Goodman contributed to this report.
Marquette Trying To Take Martin From Vols
Andy Katz discusses Marquette's interest in Tennessee coach Cuonzo Martin.